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Quasicrystalline 30 Twisted Bilayer Graphene As an Incommensurate Quasicrystalline 30◦ twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling Wei Yaoa,b, Eryin Wanga,b, Changhua Baoa,b, Yiou Zhangc, Kenan Zhanga,b, Kejie Baoc, Chun Kai Chanc, Chaoyu Chend, Jose Avilad, Maria C. Asensiod,e, Junyi Zhuc,1, and Shuyun Zhoua,b,f,1 aState Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China; bDepartment of Physics, Tsinghua University, Beijing 100084, China; cDepartment of Physics, The Chinese University of Hong Kong, Hong Kong, China; dSynchrotron SOLEIL, L’Orme des Merisiers, Saint Aubin-BP 48, 91192 Gif sur Yvette Cedex, France; eUniversite´ Paris-Saclay, L’Orme des Merisiers, Saint Aubin-BP 48, 91192 Gif sur Yvette Cedex, France; and fCollaborative Innovation Center of Quantum Matter, Beijing 100084, P. R. China Edited by Hongjie Dai, Department of Chemistry, Stanford University, Stanford, CA, and approved May 25, 2018 (received for review December 1, 2017) The interlayer coupling can be used to engineer the electronic Although the electronic structures of commensurate het- structure of van der Waals heterostructures (superlattices) to erostructures have been investigated in recent years (13–17), obtain properties that are not possible in a single material. So research on incommensurate heterostructures remains limited far research in heterostructures has been focused on commen- for two reasons. On one hand, incommensurate heterostruc- surate superlattices with a long-ranged Moire´ period. Incom- tures are difficult to be stabilized, and thus, they are quite mensurate heterostructures with rotational symmetry but not rare under natural growth conditions. On the other hand, translational symmetry (in analogy to quasicrystals) are not only it is usually assumed that the interlayer interaction is sup- rare in nature, but also the interlayer interaction has often been pressed due to the lack of phase coherence. For example, assumed to be negligible due to the lack of phase coherence. incommensurate tBLG has often been taken as a trivial com- Here we report the successful growth of quasicrystalline 30◦ bination of two noninteracting graphene layers (18–20). How ◦ twisted bilayer graphene (30 -tBLG), which is stabilized by the the electronic structure is modified in such incommensu- SCIENCES Pt(111) substrate, and reveal its electronic structure. The 30◦-tBLG rate heterostructures, with symmetry analogous to quasicrys- APPLIED PHYSICAL is confirmed by low energy electron diffraction and the interval- talline order, is a fundamental question. Here by growing ley double-resonance Raman mode at 1383 cm−1. Moreover, the epitaxial 30◦-tBLG successfully on Pt(111) substrate and reveal- emergence of mirrored Dirac cones inside the Brillouin zone of ing its electronic structure using angle-resolved photoemis- each graphene layer and a gap opening at the zone boundary sion spectroscopy (ARPES) and NanoARPES, we show that suggest that these two graphene layers are coupled via a gen- the interlayer coupling can modify the electronic structure eralized Umklapp scattering mechanism—that is, scattering of a significantly, leading to mirrored Dirac cones. Additionally, Dirac cone in one graphene layer by the reciprocal lattice vector to understand the intriguing stability that is against com- of the other graphene layer. Our work highlights the important mon belief on bilayer graphene, we performed first-principles role of interlayer coupling in incommensurate quasicrystalline calculations and found that such incommensurate 30◦-tBLG superlattices, thereby extending band structure engineering to incommensurate superstructures. Significance twisted bilayer graphene j NanoARPES j incommensurate Interlayer interaction in van der Waals heterostructures ◦ heterostructure j band structure engineering j quasicrystalline 30 -tBLG could induce many exotic phenomena. Unlike commensu- rate heterostructures, incommensurate ones have often been n van der Waals heterostructures (1), a long-ranged commen- neglected, due to the rarity in nature and the assumption of Isurate Moir´e superlattice (2–7) forms only when satisfying suppressed coherent interlayer movement of electrons. How top top 0 bottom 0 bottom top ma1 + na2 = m a1 + n a2 (8), where a1,2 and the interlayer interaction affects the electronic structure of abottom such a nonperiodic heterostructure is a fundamental ques- 1,2 are primitive lattice vectors for the top and bottom lay- ◦ ers, respectively, and m, n, m0, and n0 are integers. Twisted tion. In this work, by successfully growing 30 -twisted bilayer bilayer graphene (tBLG) can be viewed as a simple version of graphene (tBLG) as an example for incommensurate “het- top erostructure” with quasicrystalline order, we report the emer- “hetero”-structure, with a1,2 rotated by a twisting angle θt with bottom gence of mirrored Dirac cones. We identify that these mirrored respect to a1,2 . In tBLG, commensuration occurs when θt Dirac cones are a consequence of the interlayer interaction, satisfies (9, 10) showing its importance in the incommensurate structure, which has been overlooked before. These results broaden the 3p2 + 3pq + q 2=2 application range of van der Waals heterostructure for future cos θ = , [1] t 3p2 + 3pq + q 2 electronic devices. Author contributions: S.Z. designed research; W.Y., E.W., C.B., Y.Z., K.Z., K.B., C.K.C., C.C., where p and q are two coprime positive integers. Fig. 1A plots J.A., M.C.A., and J.Z. performed research; W.Y. and S.Z. analyzed data; and W.Y., J.Z., and the possible twisting angles for forming commensurate tBLG S.Z. wrote the paper. for q = 1. It is clear that commensuration easily forms around The authors declare no conflict of interest. ◦ ◦ 0 , while for larger twist angles, especially around 30 , incom- This article is a PNAS Direct Submission. mensurate superlattice is more common (11). In contrast to Published under the PNAS license. commensurate superlattice with a long-ranged period (see exam- 1 To whom correspondence may be addressed. Email: syzhou@mail.tsinghua.edu.cn or ple in Fig. 1B), incommensurate superlattice lacks a long-ranged jyzhu@phy.cuhk.edu.hk.y translational symmetry in real space while preserving the rota- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. tional symmetry; for example, 30◦-tBLG (Fig. 1C) is similar to 1073/pnas.1720865115/-/DCSupplemental. quasicrystals with a classic dodecagonal pattern (12). www.pnas.org/cgi/doi/10.1073/pnas.1720865115 PNAS Latest Articles j 1 of 6 Downloaded by guest on October 1, 2021 A incommensurate C incommensurate heterostructure work shows that distinguished from other graphene/Pt with com- commensurate (Quasicrystalline) mensurate (e.g., 2 × 2, 3 × 3) Moir´e superstructures (21), the ◦ 0 60 interface between the 30 monolayer graphene and the Pt(111) substrate is incommensurate without forming any Moir´e pattern, leading to nearly free-standing monolayer graphene (22). Fur- ther increasing the annealing temperature and time can lead to a thicker graphene sample with a new set of diffraction peaks emerging at 0◦ orientation (red arrow in Fig. 2B) coexisting with those at 30◦, and such a graphene sample is the focus of the cur- B rent work. The lattice constants extracted from LEED show that commensurate superlattice there is negligible strain (<0.2%; see SI Appendix, Fig. S1 for details) between the 30◦ and 0◦ graphene layers, and the absence of additional reconstructed diffraction spots in the LEED pat- tern further supports that they do not form commensurate super- lattice. If these diffraction peaks come from the same graphene domains, this would imply that 0◦ graphene is stacked on top of the bottom 30◦ graphene layer—namely, a 30◦-tBLG is formed. In the following, we will provide direct experimental evidence Fig. 1. Commensurate and incommensurate tBLG. (A) The distribution of for the conjectured incommensurate 30◦-tBLG from Raman all possible twisting angles θt for forming commensurate tBLG when q = 1 spectroscopy and reveal its electronic structure from ARPES in Eq. 1. The Moire´ period at corresponding twisting angles is represented measurements. by the length of the solid line (with logarithmic scale). (B) Commensurate tBLG with 7.34◦ twisting angle (indicated by the blue arrow in A), show- ing Moire´ pattern with periodic translational symmetry. Green arrows are Intervalley Double-Resonance (DR) Raman Mode. Raman spec- the Moire´ reciprocal lattice vectors. (C) Incommensurate 30◦-tBLG without troscopy is a powerful tool for characterizing the vibrational any long-ranged period (indicated by red arrow in A), showing patterns of mode in graphene (23) and can provide direct information about dodecagonal quasicrystal. the sample thickness and stacking. Fig. 2G shows a typical optical image of the as-grown sample. The optical image shows strong intensity contrast, with a darker region of ≈10 µm overlapping heterostructure is stabilized under appropriate substrate with the brighter region. The Raman spectra in Fig. 2C show conditions. stronger intensity for the darker region (red curve) than the brighter region (blue curve), suggesting that the darker region Results is thicker. The spectra for both regions show characteristic fea- Growth of 30◦-tBLG. The 30◦-tBLG sample was grown on the tures of monolayer graphene (23), in which the 2D mode shows a Pt(111) substrate by carbon segregation from the bulk sub- single Lorentzian peak with stronger intensity than the G mode. strate (21, 22). Fig. 2A shows
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